Klasificiramo preslikave, ki ohranjajo Jordanski produkt na končno razsežnih, formalno realnih, enostavnih Jordanskih algebrah. Čeprav ne privzamemo aditivnosti, se izkaže, da je vsaka tovrstna ...preslikava bodisi realno linearni avtomorfizem bodisi konstantna funkcija. Glavno dokazovalno orodje je redukcija na preslikave, ki ohranjajo ničle Jordanskega produkta.
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